The best-fitting values of the iron abundance are high with \(A_{\rm Fe} \ge 5\) , and the fits prefer changing in iron abundance which roughly increases along with the decay, resulting in an apparent correction with the reflection fraction with the p-value of 7.5\(\times 10^{-21}\) .
Such supersolar abundances also appear in the spectral fitting of other black hole X-ray binaries, e.g., GX 339-4 [1]} and Cyg X-1 [2]}.
It was suggested that the derived supersolar abundances are not physical, but may be caused by the limitation of the assumed density in the reflection model [3]}, [4]}.
Both the density and the iron abundance of the accretion disk have impacts on the emergent reflection spectrum. As the density increases, the rise in free-free absorption leads to an increase in temperature, causing extra thermal emission at soft X-ray energy \(E<10\)  keV
[3]}. This effect could become significant when the density is high (\(n_{\rm e} > 10^{19} \rm cm^{-3}\) ) (see Fig. 7 in ref[4]}), although it was emphasized that the microphysics in the current reflection models is only known to be accurate up to \(n_{\rm e} = 10^{19} \rm cm^{-3}\)  (see the reference [3]} for more details). The effect of the abundance on the reflection spectrum is studied, using the relxillCp model. The increase in the iron abundance from \(A_{\rm Fe} = 1\)  to \(A_{\rm Fe} = 10\) , will also cause the increase in the soft X-ray emission of the reflection for the highly ionized disk in the hard state (see Supplementary Figure 4a), mimicking the effect of the disk density increase.
Therefore, the soft X-ray emission could be reproduced by either high density or high abundance in the accretion disk [3]}, [4]}.
It was shown that, the high density model with the solar value of iron abundance, or the low density model with supersolar abundance, could both fit the NuSTAR spectra of Cygnus X-1 [4]}.
In the current reflection model relxillCp which is used in this work, the constant density is fixed at constant value \(n_{\rm e} = 10^{15} \rm cm^{-3}\)  , which is much lower than the typical values in the standard thin disk model [11]}, \(n_{\rm e} \ge 10^{19} \rm cm^{-3}\) .
Along with the decay of the outburst studied in this work, the radiation pressure in the inner disk should decrease and thus the gas density should increase [12]}, [3]}. Therefore, the spectral fits with the much lower and constant density in the reflection model should lead to artificially supersolar and also increasing iron abundance along with the outburst decay, consistent with the spectral fitting results in this work. Deriving the physical values and evolution of the iron abundance and disk density with the spectral fitting, however, requires new atomic data in high-density to be implemented in the reflection model, which is beyond the scope of this work.
Nonetheless, in order to demonstrate that the observed trend of the reflection fraction is physical and independent of the expected artificial correlation between the reflection fraction and the iron abundance, we tried the case of the constant iron abundance, e.g., \(A_{\rm Fe} = 5.0\) . In this case, the reflection fraction still decreases along with the outburst decay (see Supplementary Figure 4b), although fixing \(A_{\rm Fe}\)  is not supported by F-test, due to the problems we discussed above.
